I would hate to have had to carry it, these sound like little more than prairie wet spots to me, but some are saying that the water table was a lot higher before the farms broke the land, and this was all just awash in those days.
Go figure.
The Ottertail would've gotten it closer than the Buffalo.
But, putting myself in their place, one would stick with the main stem until it became impassable. That would always afford the route of least overland travel. The main stem of the Red is the Bois de Sioux, which forms the Minnesota-Dakota border south of Fargo.
The Bois de Sioux heads in a swamp that it shares with the headwaters of the Minnesota River, just north of Traverse Lake on the Minnesota-South Dakota border. But I don't believe our voyageurs (or the Norse equivalent) would have followed the Bois de Sioux this far.
About 15 miles north of the swamp, the river forks. To a traveler headed upstream, the Rabbit River would be coming in from the left (east)while the Bois de Sioux continued south into the swamp. At this point, based on a topographical map, it appears that the Bois de Sioux turns turbid and boggy. But the Rabbit seems to have a clearly defined channel to the east.
Bois de Sioux-Rabbit River junction.
The channel doesn't last long, maybe ten miles, until the stream peters out somewhere southeast of Campbell, MN. But the Rabbit has pointed them straight for Kensington and, from there, it's 40 miles overland to the stone's resting spot.
If you'll take a look at the topo above and the adjacent quads to the east and south, you'll see that the area is criss-crossed with drainage ditches. Meaning a.) that it's very flat and b.) poorly drained. Consequently, in 1362, winter snowmelt and Spring floods would have left vast portions of this terrain under water, I betcha.
Accordingly, our intrepid venturers might've been able to float further than we thought...